You can get a free transit visa on a connection under 24 hours....then get Uber to anywhere in town for 15JD each way.

Otherwise RJ lounge airside for 30JD,it's good,but not for 16 hours.

Re:checking baggage thru,generally RJ policy is not to interline bags to non RJ/OW flights on separate bookings,but the staff at TLV may apply discretion and entertain your request.